Density Functional Theory for Strongly-Interacting Electrons

Abstract

Although Kohn–Sham (KS) density functional theory (DFT) is an exact theory, able in principle to describe any interacting $N$-electron system in terms of the non-interacting Kohn–Sham model, in practice only approximate expressions for the exchange-correlation term are available. For decades, a large number of such approximations have been developed, proving enormously successful and accurate for applications in many different fields. However, there still remain important situations, of both fundamental and practical interest, for which all the commonly employed exchange-correlation functionals fail to provide an accurate description. The paradigm of such scenarios are those systems in which the electronic correlation plays the most important role. In this chapter, we show how the knowledge on the strong-interaction limit of DFT, recently formulated within the so-called strictly-correlated-electrons (SCE) formalism, can be imported into the Kohn–Sham approach and used to build approximations for the exchange-correlation energy that are able to reproduce key features of the strongly-correlated regime. We report results of the first applications of this “KS SCE” DFT approach on quasi-one-dimensional systems, showing its very good accuracy in the limits of both vanishing and infinite correlation. In the last part of the chapter, we propose a generalization of the approach for its application to more general systems.